Thanks for the suggestions!
I generously gave Pelican and Sunset Audi a lot of my money this summer when I purchased all of the things to do my timing belt. In addition to this, I found that I had several metal coolant lines that were severely rusted (PITA to get to and change), and I found a bunch of other things that needed attention when I had this thing apart. I found
this article which explains how the heater core works in these cars. I am sure that I have a little bit of flow, but I imagine that a lot of these little lines are clogged and a few are probably not.
I do not think there is an airpocket in the core. I bought an airlift system because this car has given me so much grief with the heat. I also bled it afterwards (near the heater core location) by running it for 5 minutes at 3k RPM. I know it is 100% filled.
I guess I will try an air compressor first (both ways), followed by a garden hose (both ways). If there is not a lot of crud coming out, I am thinking about using what GM recommended to get rid of their dexcool sludge (Oxalic Acid + Sodium Carbonate). Apparently it is safe for the cooling system and very effective.